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Option 4 is necessary because, when you use the search interface to estimate time series values of a forcing function, e.g., to obtain a temporal pattern of apparent primary production 'anomalies' for the ecosystem, you need to be careful about the risk of obtaining a spurious anomaly sequence that just represents measurement errors in the fitting data. Generally, if you are fitting the data to n independent time series of relative abundance, (i.e., for n of the groups), you can expect the fitting procedure to reduce the sum of squares (SS) by the proportion (n-1)/n by varying time forcing values even if there is no real time forcing effect. So if n=1, the fitting procedure can usually find a sequence of forcing values that make SS=0, but this sequence is meaningless (could be either real productivity anomalies or just spurious way of explaining measurement errors in the single abundance time series).

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The Null hypothesis distribution SSred/SSo button allows you to estimate a probability distribution for the F statistic SSreduced/SSbase under the null hypothesis that all of the deviations between model and predicted abundances are due to chance alone, i.e. under the hypothesis that there are no real productivity anomalies. The calculation of this F statistic requires a Monte-Carlo simulation procedure in order to account for autocorrelation in the model residuals that is expected even under the null hypothesis. Be warned that even if you do find a statistically significant reduction in SS by using the search procedure, this does not mean that the estimated sequence of relative primary production values is in fact 'real'. All that you can say is this: “assuming that primary production was in fact variable and that this did cause changes in relative abundance throughout the food web, then our best estimate of the historical pattern of variation is the one obtained by the fitting procedure”.

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The Null hypothesis distribution SSred/SSo button allows you to estimate a probability distribution for the F statistic SSreduced/SSbase under the null hypothesis that all of the deviations between model and predicted abundances are due to chance alone, i.e. under the hypothesis that there are no real productivity anomalies. The calculation of this F statistic requires a Monte-Carlo simulation procedure in order to account for autocorrelation in the model residuals that is expected even under the null hypothesis. Be warned that even if you do find a statistically significant reduction in SS by using the search procedure, this does not mean that the estimated sequence of relative primary production values is in fact 'real'. All that you can say is this: "assuming that primary production was in fact variable and that this did cause changes in relative abundance throughout the food web, then our best estimate of the historical pattern of variation is the one obtained by the fitting procedure".

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Use the ''Time series weight'' box to set relative weights. This represents a prior assessment by the user about relatively how variable or reliable that type of data is compared to the other reference time series (low weights imply relatively high variance or unreliable data; higher weights imply low variance or reliable data). This grid will/will not overwrite weights that were set on the ''Time series'' form.